(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V=Mn(F) be the space of all nxn matrices over F; define TA=(1/2)(A+transpose(A)) for A in V.

Verify that T is not only a linear operator on V, but is also a projection.

2. Relevant equations

A is a projection when A squared=A.

3. The attempt at a solution

I don't see how this works since clearly (1/2)(A+transpose(A)) squared does not equal (1/2)(A+transpose(A)) for all matrices.

What am I doing wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Show this is a projection on a vector space

**Physics Forums | Science Articles, Homework Help, Discussion**